Abstract This article studies the solutions of time-dependent differential inclusions which is motivated by their utility in optimization algorithms and modeling physical systems. The inclusion described a set-valued mapping having property that, for given time instant, describes maximal monotone operator. By successive application proximal operator, we construct sequence functions parameterize...

Plasticity between Th17 and Treg cells is regarded as a crucial determinant of tumor-associated immunosuppression. Classically mediate inflammatory responses through production cytokine IL17. Recently, have also been shown to acquire suppressive phenotypes in tumor microenvironment. However, the mechanism by which they such immunosuppressive properties still elusive. Here, we report that microe...

In this paper, we propose two algorithms, namely extrapolated proximal iterative hard thresholding (EPIHT) algorithm and EPIHT algorithm with line-search (EPIHT-LS), for solving `0 norm regularized wavelet frame balanced approach for image restoration. Under the theoretical framework of KurdykaLojasiewicz property, we show that the sequences generated by the two algorithms converge to a local m...

We introduce a partial proximal point algorithm for solving nuclear norm regularized matrix least squares problems with equality and inequality constraints. The inner subproblems, reformulated as a system of semismooth equations, are solved by an inexact smoothing Newton method, which is proved to be quadratically convergent under a constraint non-degeneracy condition, together with the strong ...

In the paper, we consider the problem of link prediction in time-evolving graphs. We assume that certain graph features, such as the node degree, follow a vector autoregressive (VAR) model and we propose to use this information to improve the accuracy of prediction. Our strategy involves a joint optimization procedure over the space of adjacency matrices and VAR matrices which takes into accoun...

In this paper, we consider to apply a primal-dual proximal point algorithm to the multicommodity network flow problem. A remarkable feature of the algorithm consists in how to find an approximate saddle point of the augmented Lagrangian of the problem. In particular, at each iteration, an approximate solution of the subproblem always satisfies the flow conservation equations for all commodities...

Abstract In this paper, we consider a class of structured nonconvex nonsmooth optimization problems, in which the objective function is formed by sum possibly and differentiable with Lipschitz continuous gradient, subtracted weakly convex function. This general framework allows us to tackle problems involving loss functions specific constraints, it has many applications such as signal recovery,...

In this paper, an equivalent smooth minimization for the L1 regularized least square problem is proposed. The proposed problem is a convex box-constrained smooth minimization which allows applying fast optimization methods to find its solution. Further, it is investigated that the property ”the dual of dual is primal” holds for the L1 regularized least square problem. A solver for the smooth pr...

Pseudomonotone∗ maps are a generalization of paramonotone maps which is very closely related to the cutting plane property in variational inequality problems (VIP). In this paper, we first generalize the so-called minimum principle sufficiency and the maximum principle sufficiency for VIP with multivalued maps. Then we show that pseudomonotonicity∗ of the map implies the “maximum principle suff...

Acceptable moves for the “worthwhile-to-move” incremental principle are such that “advantages to move” are higher than some fraction of “costs-to-move”. When combined with optimization, this principle gives raise to adaptive local search proximal algorithms. Convergence results are given in two distinctive cases, namely low local costs-to-move and high local costs-to-move. In this last case, on...